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Helmholtz

Benchmarks

Task NameDataset NameSOTA ResultTrend
Higher-frequency wave-field predictionHelmholtz (test)
H1 Score0.422
32
Forward PDE solvingHelmholtz
Relative Error0.0072
26
Forward PDE SolvingHelmholtz
Relative L2 Error0.025
18
PDE SolvingHelmholtz
RMSE (Helmholtz)0.222
17
Eigenvalue problem solvingHelmholtz Dimension: 6400 Precision: 1e-8
Average Computation Time (s)31.31
17
Forward PDE SolvingHelmholtz 10K-epoch
Relative L2 Error1
16
Learning PDEsHelmholtz 2D a=10
Relative L2 Error0
15
Solving PDEHelmholtz
Relative Error0.01
14
Physics-Informed PDE Solving2D Helmholtz (test)
Time (sec/iter)0.0228
14
Inverse PDE solvingHelmholtz full observations
Relative Error0.049
14
Forward PDE SolvingHelmholtz (test)
Relative H1 Error0.1385
12
Spatio-temporal PDE reconstructionHelmholtz
PDE Residual0.55
12
Solving Partial Differential EquationsHelmholtz 3D (test)
Absolute Error19.86
10
Solving Partial Differential EquationsHelmholtz 2D (test)
Absolute Error0.0384
10
PDE ReconstructionHelmholtz synthetic (test)
RMSE0.022
10
PDE ReconstructionHelmholtz 3% uniformly random measurements
Coefficient Relative L2 Error7.67
10
Inverse PDE solvingHelmholtz
Relative Error15.91
10
Neural Operator Learningδ-Helmholtz
Relative L2 Error0.0013
9
Forward PDE solvingHelmholtz Full Observation
L2 Relative Error0.0108
9
Inverse problemHelmholtz
PDE Residual0.2
9
Forward prediction2D Helmholtz
Relative L1 Error1.71
8
Shape Optimization and InversionHelmholtz
Inference Time (ms)0.47
8
Partial Differential Equation SolvingHelmholtz-2D
Error0.0088
8
Solving Constrained PDEsHelmholtz
MMSE0.14
7
Forward predictionHelmholtz Cross-equation (test)
L2 Relative Error0.0873
7
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